Question

Engineers speculate that W, the amount of weight (in units of 1000 pounds) that a certain span of a bridge can withstand without structural damage resulting, is normally distributed with mean 400 and standard deviation 40. Suppose that the weight (again, in units of 1000 pounds) of a car is a random variable with mean 3 and standard deviation.3. Approximately how many cars would have to be on the bridge span for the probability of structural damage to exceed .1?

A. 106
B. 123
C. 120
D. 115
E. 117

Answer 1

n = 116.2 ≈ 117

Option E) 117 is the correct answer.

Explanation:

Given the data in the question;

Exceed = 0.1

{ 1 - 0.1 = 0.9 }

normal table value at 0.9 = - 1.285

Normal table;

hence

( y - 400 ) / 40 = -1.285

y - 400 = -51.4

y = 400 - 51.4

y = 348.6

so,

348.6 = ∈(y) = ∈[ ⁿ∑
`_{i=1` X
`_i` ]

348.6 = n.∈( X
`_i` )

we substitute

348.6 = n × 3

n = 348.6 / 3

n = 116.2 ≈ 117 { roundup since we talking of number of cars i.e sample size }

Option E) 117 is the correct answer.